A false sillogism, indeed, but that's how you make headlines. And btw doesn't make the discovery any less exciting.
Except for the Higgs boson, the usual picture is that matter particles are fermions and force mediators are bosons:
https://upload.wikimedia.org/wikipedia/commons/thumb/0/00/St...
One interpretation I've seen is that there are 4 Higgs bosons, three of which are "swallowed" by 3 of the the weak-force bosons which and become the W+ W- and Z. The remaining 4th Higgs boson (the 4th degree of freedom of the Higgs field) is what we can see, together with the 4th weak-force boson, the photon, which remains massless.
So I think it's reasonable to consider that the Higgs boson belongs to the weak force.
Is this correct? And if so, does this fact matter in deciding whether to say Higgs == fundamental force?
If it were the same at all space time points it would be a constant, and rather boring (more like a cosmological constant).
EDIT: btw, you got the scalar/vector definition wrong.
A scalar field is one where each point in space can be labeled by a single scalar (not the same vale for all points), for example a temperature reading at different locations.
A vector field assign a distinct vector (i.e. magnitude and direction) to each point in space, for example if you take a compass around the globe you can assign to each location the direction the compass arrow is pointing.
A tensor field is of course assign a tensor to every point in space. I only have rough understanding of what a tensor is, as a first approximation it can be understood as a matrix with special properties.